"That was a good, gutsy win," Coyotes coach Rick Tocchet said. "We picked up the pace, we had puck possession and guys started believing what we were doing out there."

The 19-year-old Keller also had the winner Dec. 22 against Washington.

Nick Cousins scored twice for Arizona, which entered the game with the worst record in the NHL. Cousins' second goal tied it with 18.3 seconds remaining in regulation after Arizona pulled goalie Antti Raanta for an extra attacker.

"With the goalie pulled anything can happen, so it was nice to get one there," Cousins said. "I think they were on their heels there in the third period and that was probably one of our better periods of the season."

Though Minnesota scored the first three goals, the Wild admitted after the game it didn't feel like a 3-0 lead. Minnesota was outshot through two periods and was sloppy on both ends of the ice.

"I don't know how to explain it. It shouldn't happen. It can't happen," said Wild forward Zach Parise. "Right now in the race that we're in and that we're going to be in for the rest of the year, it's a tough point to lose."

Staal opened the scoring with 2:47 to play in the first period with his team-leading 24th goal. Staal fired a pass from Jared Spurgeon top shelf past Raanta.

Cullen, the Wild's 41-year-old forward, made it 2-0 early in the second period on a breakaway.

The Wild were without defenseman Jonas Brodin on Thursday after Brodin suffered a broken hand Tuesday against St. Louis. In Brodin's absences, Minnesota's young defenseman such as Reilly and Gustav Olofsson will have a chance to gain some additional ice time.

Reilly took advantage Thursday, scoring his first goal of the season and just the third of his NHL career. Reilly grabbed a loose puck out of the air and set it on the ice before firing from the faceoff circle past Raanta.

Arizona clawed back with three unanswered goals in regulation. Cousins buried a cross-ice pass from Alex Goligoski for the Coyotes' first goal midway through the second period. Connaughton's goal 8:02 into the third made it a one-goal game.

The Coyotes came to St. Paul with just 12 wins on the season, while Minnesota's 27 wins and 59 points had the Wild hovering on the cusp of the top eight spots in the Western Conference.

Thursday's overtime loss was a point the Wild felt they should have had.

"That's not good enough. Pretty simple. That was the message after the game and the message from here on in," said Wild coach Bruce Boudreau. "You're fighting for your playoff lives and you come up and you blow a 3-0 lead to a team that isn't going to be in the playoffs. You can't be successful if you do that."